Here in Texas, our math standards, the Texas Essential Knowledge and Skills (TEKS), changed dramatically this year, and teachers are facing a steep learning curve. For many of our kiddos, it also means they have gaps in their learning because some standards have been shifted between grades and some are brand new. For example, there are now 3rd grade TEKS that are fundamental to understanding the 4th grade TEKS, but our current 4th graders never learned those concepts because they didn’t exist with the old standards. This situation makes it more important than ever that teachers know not only their own standards, but the standards in the grades before and after their grade level. To read how the fraction TEKS progress from 1st grade through 5th grade, check out this post.
The language of the new fraction-related TEKS is very similar to the wording the the CCSSM, and it has teachers scratching their heads. There is new emphasis on the unit fraction (1/b). Simply put, a unit fraction is a fraction with a numerator of 1–it is one part of a whole that has been divided into b equal parts. So 1/4, 1/6, and 1/20 are all unit fractions. Along with that, students are expected to understand the meaning of the numerator and the denominator. Today, I killed two birds with one stone using a classic Marilyn Burns Game, Cover Up, from her book About Teaching Mathematics. I focused on the meaning of the denominator through the math talk we engaged in while playing.
We used plastic fraction tile kits to play, but you can have students create a fraction kit by folding paper strips. You also need a fraction cube with faces labeled to match your pieces. Ours was labeled 1/2, 1/3, 1/4, 1/6, 1/6, 1/12 and 1/12. Notice that there are more faces labeled with the smaller fractions. If you don’t have a fraction cube, you can create one using a cube with blank faces, or you can put stickers labeled with fractions on the faces of a standard number cube.
To summarize the game, players try to cover the whole with smaller fractions. They must cover it exactly–no overlap. We started by laying out the red whole piece (the piece labeled 1). Notice that I had my kiddos use dry erase markers to draw a number line under the fraction bar to connect with the idea that our whole is the space between 0 and 1 on the number line. That understanding has been an ongoing battle, and you can read more about it here. I rolled the fraction cube and got 1/3, so I placed the 1/3 piece on top of my whole. Here’s where I introduced the math talk. I modeled that for each turn, students were expected to (1) read the fraction and (2) explain the meaning of the denominator. For my roll of 1/3, it sounded like this: I have one third. The denominator of 3 means that the whole is divided into 3 equal parts. That might seem easy enough, but it was actually enough of a struggle for the students that I wrote the second sentence on my white board easel for them to refer to.
We all did that for our first round of turns. When it came back to me, I introduced the next level of math talk. This time around, and for the rest of the game, we would compare the fraction we just laid down with the fraction before it. I rolled 1/6 and laid it on the whole. I still had to read my fraction and explain the denominator: I have one sixth. The denominator of 6 means the whole is divided into 6 equal parts. Next, I compared my fractions: 1/3 is greater than 1/6, because with three equal parts the parts are bigger than with six equal parts. More parts means smaller pieces. Again, this was really a struggle for them, but we got lots of practice as the game progressed. For example, if I rolled 1/4 on my next turn, I would read my fraction, explain the denominator, and compare 1/6 and 1/4.
Combining a math game with math talk put the fun in practicing a fundamental concept!